Visit Japan Web: Blue screen

Hello everyone.

I am flying out of Japan tomorrow and returning in a week.
I just did the Visit Japan Web pre-registration in advance.
My name on my passport includes a first name and middle name, which I don’t use at all in daily life (in Europe I don’t know anyone who actually uses their middle name). So, naturally, all my European cards like health insurance card include only my first name. That’s why my vaccine certificate includes only my first name and not my middle name.
On visit Japan web itself, I registered my full name like on my passport.

I submitted the certificate this morning and the screen turned blue. Am I good to go? Should I write the full name with a pen or do I just leave it as such? It seems that blue screen means it’s accepted so it seems like my first name only is satisfactory but I wanted to ask just in case.
When reentering Japan do they just look at the screen or do I need to print it and bring it ?